First off the Armada is not a small SUV as most posters seem to think. It is based on the Titan truck platform and is a fairly stout vehicle. Payloads range from 14-1700lbs depending on model. Not to be confused with the smaller Pathfinder which also used to have Armada in its name.
That being said a 32-36', 7800lbs empty trailer is way too much for the Armada.
As mentioned, you will be payload limited. Load the family into the vehicle and go to a scale. Subtract the loaded weight from your GVWR and that's what you have left for tongue and hitch weight. A 6k loaded tt is probably a good estimate.